« on: 27/03/2020 16:14:54 »
As point out by Halc, it isn't needed here.With D moving at 0.5c towards the Earth and the Earth receding at 0.2c, the closing speed between D and the Earth, according to B is 0.3c, at which rate, it will take 20 years for D to reach the Earth.That doesn't seem like relativistic velocity addition.
To make the scenario perfectly symmetrical using those numbers, in B frame D should aim to planet Y which is 10 lightyears away. At speed of 0.5c, it will take 20 years to reach planet Y.
Example, You have Alice, Bob, and Charlie.
Alice "stays home", while as measured by her, Bob and Charlie both head off in opposite directions at 0.5c
According to Alice, With Bob going in one direction and Charlie in the other, the distance between them is increasing at a rate of 0.5c + 0.5c = 1c . After 1 hr they will be 1 light hr apart from each other ( Bob will be 0.5 light hr from Alice in one direction, and Charlie 0.5 light hr from Alice in the the Other.) etc.
For Bob to get the relative speed between himself and Charlie, he adds the 0.5c he measures relative to Alice, to the 0.5c Alice measures as the relative velocity between herself and Charlie, using relativistic velocity addition.
(.05c+..5c)/1(1+0.5c(0.5c)/c^2) = 0.8c
The difference between Charlie's velocity and Alice's velocity as measured by Bob is 0.8c-0.5c = 0.3c
After 1 hr ( by Bob's clock) Bob measures Alice to be 0.5 light hr away, and Charlie as being 0.8 light hr way. A difference of 0.3 light hr.
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